The present invention relates to methods for driving electro-optic displays, especially bistable electro-optic displays, and to apparatus for use in such methods. Some aspects of the present invention relate to driving methods which may allow for reduced “ghosting” and edge effects. Other aspects of the present invention relate to reduction of noise in the images on electro-optic displays; such noise may include that referred to as “grain” or “mottle” and is believed (although the invention is in no way limited by this belief) to be due to non-uniformities in the electro-optic material itself. This invention is especially, but not exclusively, intended for use with particle-based electrophoretic displays in which one or more types of electrically charged particles are present in a fluid and are moved through the fluid under the influence of an electric field to change the appearance of the display.
The term “electro-optic”, as applied to a material or a display, is used herein in its conventional meaning in the imaging art to refer to a material having first and second display states differing in at least one optical property, the material being changed from its first to its second display state by application of an electric field to the material. Although the optical property is typically color perceptible to the human eye, it may be another optical property, such as optical transmission, reflectance, luminescence or, in the case of displays intended for machine reading, pseudo-color in the sense of a change in reflectance of electromagnetic wavelengths outside the visible range.
The term “gray state” is used herein in its conventional meaning in the imaging art to refer to a state intermediate two extreme optical states of a pixel, and does not necessarily imply a black-white transition between these two extreme states. For example, several of the E Ink patents and published applications referred to below describe electrophoretic displays in which the extreme states are white and deep blue, so that an intermediate “gray state” would actually be pale blue. Indeed, as already mentioned, the change in optical state may not be a color change at all. The terms “black” and “white” may be used hereinafter to refer to the two extreme optical states of a display, and should be understood as normally including extreme optical states which are not strictly black and white, for example the aforementioned white and dark blue states. The term “monochrome” may be used hereinafter to denote a drive scheme which only drives pixels to their two extreme optical states with no intervening gray states.
The terms “bistable” and “bistability” are used herein in their conventional meaning in the art to refer to displays comprising display elements having first and second display states differing in at least one optical property, and such that after any given element has been driven, by means of an addressing pulse of finite duration, to assume either its first or second display state, after the addressing pulse has terminated, that state will persist for at least several times, for example at least four times, the minimum duration of the addressing pulse required to change the state of the display element. It is shown in U.S. Pat. No. 7,170,670 that some particle-based electrophoretic displays capable of gray scale are stable not only in their extreme black and white states but also in their intermediate gray states, and the same is true of some other types of electro-optic displays. This type of display is properly called “multi-stable” rather than bistable, although for convenience the term “bistable” may be used herein to cover both bistable and multi-stable displays.
The term “impulse” is used herein in its conventional meaning of the integral of voltage with respect to time. However, some bistable electro-optic media act as charge transducers, and with such media an alternative definition of impulse, namely the integral of current over time (which is equal to the total charge applied) may be used. The appropriate definition of impulse should be used, depending on whether the medium acts as a voltage-time impulse transducer or a charge impulse transducer.
Much of the discussion below will focus on methods for driving one or more pixels of an electro-optic display through a transition from an initial gray level to a final gray level (which may or may not be different from the initial gray level). The term “waveform” will be used to denote the entire voltage against time curve used to effect the transition from one specific initial gray level to a specific final gray level. Typically such a waveform will comprise a plurality of waveform elements; where these elements are essentially rectangular (i.e., where a given element comprises application of a constant voltage for a period of time); the elements may be called “pulses” or “drive pulses”. The term “drive scheme” denotes a set of waveforms sufficient to effect all possible transitions between gray levels for a specific display. A display may make use of more than one drive scheme; for example, the aforementioned U.S. Pat. No. 7,012,600 teaches that a drive scheme may need to be modified depending upon parameters such as the temperature of the display or the time for which it has been in operation during its lifetime, and thus a display may be provided with a plurality of different drive schemes to be used at differing temperature etc. A set of drive schemes used in this manner may be referred to as “a set of related drive schemes.” It is also possible, as described in several of the aforementioned MEDEOD applications, to use more than one drive scheme simultaneously in different areas of the same display, and a set of drive schemes used in this manner may be referred to as “a set of simultaneous drive schemes.”
Several types of electro-optic displays are known. One type of electro-optic display is a rotating bichromal member type as described, for example, in U.S. Pat. Nos. 5,808,783; 5,777,782; 5,760,761; 6,054,071 6,055,091; 6,097,531; 6,128,124; 6,137,467; and 6,147,791 (although this type of display is often referred to as a “rotating bichromal ball” display, the term “rotating bichromal member” is preferred as more accurate since in some of the patents mentioned above the rotating members are not spherical). Such a display uses a large number of small bodies (typically spherical or cylindrical) which have two or more sections with differing optical characteristics, and an internal dipole. These bodies are suspended within liquid-filled vacuoles within a matrix, the vacuoles being filled with liquid so that the bodies are free to rotate. The appearance of the display is changed by applying an electric field thereto, thus rotating the bodies to various positions and varying which of the sections of the bodies is seen through a viewing surface. This type of electro-optic medium is typically bistable.
Another type of electro-optic display uses an electrochromic medium, for example an electrochromic medium in the form of a nanochromic film comprising an electrode formed at least in part from a semi-conducting metal oxide and a plurality of dye molecules capable of reversible color change attached to the electrode; see, for example O'Regan, B., et al., Nature 1991, 353, 737; and Wood, D., Information Display, 18(3), 24 (March 2002). See also Bach, U., et al., Adv. Mater., 2002, 14(11), 845. Nanochromic films of this type are also described, for example, in U.S. Pat. Nos. 6,301,038; 6,870,657; and 6,950,220. This type of medium is also typically bistable.
Another type of electro-optic display is an electro-wetting display developed by Philips and described in Hayes, R. A., et al., “Video-Speed Electronic Paper Based on Electrowetting”, Nature, 425, 383-385 (2003). It is shown in U.S. Pat. No. 7,420,549 that such electro-wetting displays can be made bistable.
One type of electro-optic display, which has been the subject of intense research and development for a number of years, is the particle-based electrophoretic display, in which a plurality of charged particles move through a fluid under the influence of an electric field. Electrophoretic displays can have attributes of good brightness and contrast, wide viewing angles, state bistability, and low power consumption when compared with liquid crystal displays. Nevertheless, problems with the long-term image quality of these displays have prevented their widespread usage. For example, particles that make up electrophoretic displays tend to settle, resulting in inadequate service-life for these displays.
As noted above, electrophoretic media require the presence of a fluid. In most prior art electrophoretic media, this fluid is a liquid, but electrophoretic media can be produced using gaseous fluids; see, for example, Kitamura, T., et al., “Electrical toner movement for electronic paper-like display”, IDW Japan, 2001, Paper HCS1-1, and Yamaguchi, Y, et al., “Toner display using insulative particles charged triboelectrically”, IDW Japan, 2001, Paper AMD4-4). See also U.S. Pat. Nos. 7,321,459 and 7,236,291. Such gas-based electrophoretic media appear to be susceptible to the same types of problems due to particle settling as liquid-based electrophoretic media, when the media are used in an orientation which permits such settling, for example in a sign where the medium is disposed in a vertical plane. Indeed, particle settling appears to be a more serious problem in gas-based electrophoretic media than in liquid-based ones, since the lower viscosity of gaseous suspending fluids as compared with liquid ones allows more rapid settling of the electrophoretic particles.
Numerous patents and applications assigned to or in the names of the Massachusetts Institute of Technology (MIT) and E Ink Corporation describe various technologies used in encapsulated electrophoretic and other electro-optic media. Such encapsulated media comprise numerous small capsules, each of which itself comprises an internal phase containing electrophoretically-mobile particles in a fluid medium, and a capsule wall surrounding the internal phase. Typically, the capsules are themselves held within a polymeric binder to form a coherent layer positioned between two electrodes. The technologies described in the these patents and applications include:                (a) Electrophoretic particles, fluids and fluid additives; see for example U.S. Pat. Nos. 7,002,728; and 7,679,814;        (b) Capsules, binders and encapsulation processes; see for example U.S. Pat. Nos. 6,922,276; and 7,411,719;        (c) Films and sub-assemblies containing electro-optic materials; see for example U.S. Pat. Nos. 6,982,178; and 7,839,564;        (d) Backplanes, adhesive layers and other auxiliary layers and methods used in displays; see for example U.S. Pat. Nos. 7,116,318; and 7,535,624;        (e) Color formation and color adjustment; see for example U.S. Pat. No. 7,075,502; and U.S. Patent Application Publication No. 2007/0109219;        (f) Methods for driving displays; see the aforementioned MEDEOD applications;        (g) Applications of displays; see for example U.S. Pat. Nos. 7,312,784; and 8,009,348; and        (h) Non-electrophoretic displays, as described in U.S. Pat. Nos. 6,241,921; 6,950,220; 7,420,549 and 8,319,759; and U.S. Patent Application Publication No. 2012/0293858.        
Many of the aforementioned patents and applications recognize that the walls surrounding the discrete microcapsules in an encapsulated electrophoretic medium could be replaced by a continuous phase, thus producing a so-called polymer-dispersed electrophoretic display, in which the electrophoretic medium comprises a plurality of discrete droplets of an electrophoretic fluid and a continuous phase of a polymeric material, and that the discrete droplets of electrophoretic fluid within such a polymer-dispersed electrophoretic display may be regarded as capsules or microcapsules even though no discrete capsule membrane is associated with each individual droplet; see for example, the aforementioned U.S. Pat. No. 6,866,760. Accordingly, for purposes of the present application, such polymer-dispersed electrophoretic media are regarded as sub-species of encapsulated electrophoretic media.
A related type of electrophoretic display is a so-called “microcell electrophoretic display”. In a microcell electrophoretic display, the charged particles and the fluid are not encapsulated within microcapsules but instead are retained within a plurality of cavities formed within a carrier medium, typically a polymeric film. See, for example, U.S. Pat. Nos. 6,672,921 and 6,788,449, both assigned to Sipix Imaging, Inc.
Although electrophoretic media are often opaque (since, for example, in many electrophoretic media, the particles substantially block transmission of visible light through the display) and operate in a reflective mode, many electrophoretic displays can be made to operate in a so-called “shutter mode” in which one display state is substantially opaque and one is light-transmissive. See, for example, U.S. Pat. Nos. 5,872,552; 6,130,774; 6,144,361; 6,172,798; 6,271,823; 6,225,971; and 6,184,856. Dielectrophoretic displays, which are similar to electrophoretic displays but rely upon variations in electric field strength, can operate in a similar mode; see U.S. Pat. No. 4,418,346. Other types of electro-optic displays may also be capable of operating in shutter mode. Electro-optic media operating in shutter mode may be useful in multi-layer structures for full color displays; in such structures, at least one layer adjacent the viewing surface of the display operates in shutter mode to expose or conceal a second layer more distant from the viewing surface.
An encapsulated electrophoretic display typically does not suffer from the clustering and settling failure mode of traditional electrophoretic devices and provides further advantages, such as the ability to print or coat the display on a wide variety of flexible and rigid substrates. (Use of the word “printing” is intended to include all forms of printing and coating, including, but without limitation: pre-metered coatings such as patch die coating, slot or extrusion coating, slide or cascade coating, curtain coating; roll coating such as knife over roll coating, forward and reverse roll coating; gravure coating; dip coating; spray coating; meniscus coating; spin coating; brush coating; air knife coating; silk screen printing processes; electrostatic printing processes; thermal printing processes; ink jet printing processes; electrophoretic deposition (See U.S. Pat. No. 7,339,715); and other similar techniques.) Thus, the resulting display can be flexible. Further, because the display medium can be printed (using a variety of methods), the display itself can be made inexpensively.
Other types of electro-optic media may also be used in the displays of the present invention.
The bistable or multi-stable behavior of particle-based electrophoretic displays, and other electro-optic displays displaying similar behavior (such displays may hereinafter for convenience be referred to as “impulse driven displays”), is in marked contrast to that of conventional liquid crystal (“LC”) displays. Twisted nematic liquid crystals are not bi- or multi-stable but act as voltage transducers, so that applying a given electric field to a pixel of such a display produces a specific gray level at the pixel, regardless of the gray level previously present at the pixel. Furthermore, LC displays are only driven in one direction (from non-transmissive or “dark” to transmissive or “light”), the reverse transition from a lighter state to a darker one being effected by reducing or eliminating the electric field. Finally, the gray level of a pixel of an LC display is not sensitive to the polarity of the electric field, only to its magnitude, and indeed for technical reasons commercial LC displays usually reverse the polarity of the driving field at frequent intervals. In contrast, bistable electro-optic displays act, to a first approximation, as impulse transducers, so that the final state of a pixel depends not only upon the electric field applied and the time for which this field is applied, but also upon the state of the pixel prior to the application of the electric field.
Whether or not the electro-optic medium used is bistable, to obtain a high-resolution display, individual pixels of a display must be addressable without interference from adjacent pixels. One way to achieve this objective is to provide an array of non-linear elements, such as transistors or diodes, with at least one non-linear element associated with each pixel, to produce an “active matrix” display. An addressing or pixel electrode, which addresses one pixel, is connected to an appropriate voltage source through the associated non-linear element. Typically, when the non-linear element is a transistor, the pixel electrode is connected to the drain of the transistor, and this arrangement will be assumed in the following description, although it is essentially arbitrary and the pixel electrode could be connected to the source of the transistor. Conventionally, in high resolution arrays, the pixels are arranged in a two-dimensional array of rows and columns, such that any specific pixel is uniquely defined by the intersection of one specified row and one specified column. The sources of all the transistors in each column are connected to a single column electrode, while the gates of all the transistors in each row are connected to a single row electrode; again the assignment of sources to rows and gates to columns is conventional but essentially arbitrary, and could be reversed if desired. The row electrodes are connected to a row driver, which essentially ensures that at any given moment only one row is selected, i.e., that there is applied to the selected row electrode a voltage such as to ensure that all the transistors in the selected row are conductive, while there is applied to all other rows a voltage such as to ensure that all the transistors in these non-selected rows remain non-conductive. The column electrodes are connected to column drivers, which place upon the various column electrodes voltages selected to drive the pixels in the selected row to their desired optical states. (The aforementioned voltages are relative to a common front electrode which is conventionally provided on the opposed side of the electro-optic medium from the non-linear array and extends across the whole display.) After a pre-selected interval known as the “line address time” the selected row is deselected, the next row is selected, and the voltages on the column drivers are changed so that the next line of the display is written. This process is repeated so that the entire display is written in a row-by-row manner.
It might at first appear that the ideal method for addressing such an impulse-driven electro-optic display would be so-called “general grayscale image flow” in which a controller arranges each writing of an image so that each pixel transitions directly from its initial gray level to its final gray level. However, inevitably there is some error in writing images on an impulse-driven display. Some such errors encountered in practice include:
(a) Prior State Dependence; With at least some electro-optic media, the impulse required to switch a pixel to a new optical state depends not only on the current and desired optical state, but also on the previous optical states of the pixel.
(b) Dwell Time Dependence; With at least some electro-optic media, the impulse required to switch a pixel to a new optical state depends on the time that the pixel has spent in its various optical states. The precise nature of this dependence is not well understood, but in general, more impulse is required the longer the pixel has been in its current optical state.
(c) Temperature Dependence; The impulse required to switch a pixel to a new optical state depends heavily on temperature.
(d) Humidity Dependence; The impulse required to switch a pixel to a new optical state depends, with at least some types of electro-optic media, on the ambient humidity.
(e) Mechanical Uniformity; The impulse required to switch a pixel to a new optical state may be affected by mechanical variations in the display, for example variations in the thickness of an electro-optic medium or an associated lamination adhesive. Other types of mechanical non-uniformity may arise from inevitable variations between different manufacturing batches of medium, manufacturing tolerances and materials variations.
Voltage Errors; The actual impulse applied to a pixel will inevitably differ slightly from that theoretically applied because of unavoidable slight errors in the voltages delivered by drivers.
General grayscale image flow suffers from an “accumulation of errors” phenomenon. For example, imagine that temperature dependence results in a 0.2 L* (where L* has the usual CIE definition:L*=116(R/R0)1/3−16,where R is the reflectance and R0 is a standard reflectance value) error in the positive direction on each transition. After fifty transitions, this error will accumulate to 10 L*. Perhaps more realistically, suppose that the average error on each transition, expressed in terms of the difference between the theoretical and the actual reflectance of the display is ±0.2 L*. After 100 successive transitions, the pixels will display an average deviation from their expected state of 2 L*; such deviations are apparent to the average observer on certain types of images.
This accumulation of errors phenomenon applies not only to errors due to temperature, but also to errors of all the types listed above. As described in the aforementioned U.S. Pat. No. 7,012,600, compensating for such errors is possible, but only to a limited degree of precision. For example, temperature errors can be compensated by using a temperature sensor and a lookup table, but the temperature sensor has a limited resolution and may read a temperature slightly different from that of the electro-optic medium. Similarly, prior state dependence can be compensated by storing the prior states and using a multi-dimensional transition matrix, but controller memory limits the number of states that can be recorded and the size of the transition matrix that can be stored, placing a limit on the precision of this type of compensation.
Thus, general grayscale image flow requires very precise control of applied impulse to give good results, and empirically it has been found that, in the present state of the technology of electro-optic displays, general grayscale image flow is infeasible in a commercial display.
It will be appreciated that, whether or not an active matrix backplane is used, updating of a display requires the preparation of some form of bitmap to indicate the desired final gray levels of every pixel in the display. On the other hand, in many cases data to be shown on the display is stored in a non-bitmap form; for example, electronic books and similar documents are often stored in a text-based form, for example as simple ASCII text, as an “epub” or “mobi” word processing file or as a text mode portable document file. Other data to be displayed may be stored as a spreadsheet or presentation file, or as a compressed image or video file. Conversion of these various stored formats to appropriate bitmaps for display (usually known as “pre-rendering”) makes major demands upon the data processing capabilities of the display electronics, especially in the case of portable electronic displays which typically have substantially lower computing power than a desktop or laptop personal computer. Pre-rendering of color images is makes especially large demands upon data processing capabilities. Furthermore, since users expect E-book readers and similar displays to respond essentially instantly to user input, in many cases (as for example when a reader is presented with a menu listing several possible choices, and which image will appear next depends upon the selected item on the menu) it is necessary for the display to pre-render several images in order to avoid delay in presenting the next image after a choice is made by the user. Such pre-rendering of multiple images, many of which may never be displayed, occupies a large amount of memory space and increases the power consumption of the display, thus reducing the available interval between battery charges in the case of a portable, battery-powered display. A first aspect of the present invention relates to reducing or eliminating the problems.
A second aspect of the present invention relates to reduction of noise in images on electro-optic displays. In practice, it is found that many electro-optic displays suffer from spatial noise, in the sense that different areas of the display exhibit different gray levels even though the areas are driven using the same drive scheme and thus experience the same waveforms. At least part of such noise appears to be due to non-uniformities in the electro-optic layer, i.e., grain artifacts. Also often present are “streak” defects which manifest themselves as elongate areas having electro-optic responses differing from those of the surrounding areas. Such grain and streak defects may, if sufficiently severe, require that part of the electro-optic medium be discarded, and the defects are thus a significant factor in yield losses in the production of electro-optic displays. Some reduction in noise and defects can be achieved by careful choice of the waveforms and drive schemes to be used in driving the display but such reduction is limited and grain and streaks are still of major concern in the manufacture of electro-optic displays.
A second aspect of the present invention seeks to provide methods for driving electro-optic displays to allow for more effective correction of noise than prior art methods.
A third aspect of the present invention relates to use of multiple drive schemes. Under some circumstances, it may be desirable for a single display to make use of multiple drive schemes. For example, a display capable of more than two gray levels may make use of a gray scale drive scheme (“GSDS”) which can effect transitions between all possible gray levels, and a monochrome drive scheme (“MDS”) which effects transitions only between two gray levels, the MDS providing quicker rewriting of the display that the GSDS. The MDS is used when all the pixels which are being changed during a rewriting of the display are effecting transitions only between the two gray levels used by the MDS. For example, the aforementioned U.S. Pat. No. 7,119,772 describes a display in the form of an electronic book or similar device capable of displaying gray scale images and also capable of displaying a monochrome dialogue box which permits a user to enter text relating to the displayed images. When the user is entering text, a rapid MDS is used for quick updating of the dialogue box, thus providing the user with rapid confirmation of the text being entered. On the other hand, when the entire gray scale image shown on the display is being changed, a slower GSDS is used.
Alternatively, a display may make use of a GSDS simultaneously with a “direct update” drive scheme (“DUDS”). The DUDS may have two or more than two gray levels, typically fewer than the GSDS, but the most important characteristic of a DUDS is that transitions are handled by a simple unidirectional drive from the initial gray level to the final gray level, as opposed to the “indirect” transitions often used in a GSDS, where in at least some transitions the pixel is driven from an initial gray level to one extreme optical state, then in the reverse direction to a final gray level; in some cases, the transition may be effected by driving from the initial gray level to one extreme optical state, thence to the opposed extreme optical state, and only then to the final extreme optical state—see, for example, the drive scheme illustrated in FIGS. 11A and 11B of the aforementioned U.S. Pat. No. 7,012,600. Thus, present electrophoretic displays may have an update time in grayscale mode of about two to three times the length of a saturation pulse (where “the length of a saturation pulse” is defined as the time period, at a specific voltage, that suffices to drive a pixel of a display from one extreme optical state to the other), or approximately 700-900 milliseconds, whereas a DUDS has a maximum update time equal to the length of the saturation pulse, or about 200-300 milliseconds.
Variation in drive schemes is, however, not confined to differences in the number of gray levels used. For example, drive schemes may be divided into global drive schemes, where a drive voltage is applied to every pixel in the region to which the global update drive scheme (more accurately referred to as a “global complete” or “GC” drive scheme) is being applied (which may be the whole display or some defined portion thereof) and partial update (or local) drive schemes, where a drive voltage is applied only to pixels that are undergoing a non-zero transition (i.e., a transition in which the initial and final gray levels differ from each other), but no drive voltage is applied during zero transitions (in which the initial and final gray levels are the same). An intermediate form a drive scheme (designated a “global limited” or “GL” drive scheme) is similar to a GC drive scheme except that no drive voltage is applied to a pixel which is undergoing a zero, white-to-white transition. In, for example, a display used as an electronic book reader, displaying black text on a white background, there are numerous white pixels, especially in the margins and between lines of text which remain unchanged from one page of text to the next; hence, not rewriting these white pixels substantially reduces the apparent “flashiness” of the display rewriting. However, certain problems remain in this type of GL drive scheme. Firstly, as discussed in detail in some of the aforementioned MEDEOD applications, bistable electro-optic media are typically not completely bistable, and pixels placed in one extreme optical state gradually drift, over a period of minutes to hours, towards an intermediate gray level. In particular, pixels driven white slowly drift towards a light gray color. Hence, if in a local drive scheme a white pixel is allowed to remain undriven through a number of page turns, during which other white pixels (for example, those forming parts of the text characters) are driven, the freshly updated white pixels will be slightly lighter than the undriven white pixels, and eventually the difference will become apparent even to an untrained user.
Secondly, when an undriven pixel lies adjacent a pixel which is being updated, a phenomenon known as “blooming” occurs, in which the driving of the driven pixel causes a change in optical state over an area slightly larger than that of the driven pixel, because the electro-optic medium lying between two pixels sees voltages that are intermediate the voltages applied to the two pixels. In addition, some electro-optic media, especially electrophoretic media, react asymmetrically to applied voltages such that if one pixel is driven with a pulse of one polarity and then with a pulse of the opposed polarity, while an adjacent pixel is undriven throughout, a visible edge is left between the two pixels. Such blooming manifests itself as edge effects along the edges where the undriven pixels lie adjacent driven pixels. Similar edge effects occur when using regional updates (where only a particular region of the display is updated, for example to show an image), except that with regional updates the edge effects occur at the boundary of the region being updated. Over time, such edge effects become visually distracting and must be cleared. Hitherto, such edge effects (and the effects of color drift in undriven white pixels) have typically been removed by using a single GC update at intervals. Unfortunately, use of such an occasional GC update reintroduces the problem of a “flashy” update, and indeed the flashiness of the update may be heightened by the fact that the flashy update only occurs at long intervals.
A third aspect of the present invention relates to reducing or eliminating the problems discussed above while still avoiding so far as possible flashy updates. However, there is an additional complication in attempting to solve the aforementioned problems, namely the need for overall DC balance. As discussed in many of the aforementioned MEDEOD applications, the electro-optic properties and the working lifetime of displays may be adversely affected if the drive schemes used are not substantially DC balanced (i.e., if the algebraic sum of the impulses applied to a pixel during any series of transitions beginning and ending at the same gray level is not close to zero). See especially the aforementioned U.S. Pat. No. 7,453,445, which discusses the problems of DC balancing in so-called “heterogeneous loops” involving transitions carried out using more than one drive scheme. A DC balanced drive scheme ensures that the total net impulse bias at any given time is bounded (for a finite number of gray states). In a DC balanced drive scheme, each optical state of the display is assigned an impulse potential (IP) and the individual transitions between optical states are defined such that the net impulse of the transition is equal to the difference in impulse potential between the initial and final states of the transition. In a DC balanced drive scheme, any round trip net impulse is required to be substantially zero.
Accordingly, the third aspect of the present invention seeks to provide methods for driving electro-optic displays to reduce the aforementioned visible edge effects.